Research in Linear Algebra with Undergraduates David Strong Pepperdine University

BACKGROUND & HOW I STARTED My university values work with students, but not as much as publications. I had a few ideas about work I might do, but didn’t do anything about them until after tenured. (I worked on projects that were too advanced for students and which led to publications.) My experience is that most undergraduate research projects don’t lead to a publication. To me, that’s acceptable—the project is more for the experience of the students.

BACKGROUND & HOW I STARTED I’ve worked on nine projects with sixteen students since being tenured in All (except one) students were in classes with me, and I invited them to work with me. (I invited one student to work with me based on a colleague’s recommendation—this turned out to be the weakest of all of my students.) The majority of the students were math majors, but a few were from CS and Physics. Most were juniors and seniors, but a couple were well qualified sophomores.

GOALS FOR MY STUDENTS Develop mathematical breadth and depth. Become more persistent and careful problem solvers. Learn how to ask meaningful questions. Become more: Creative Independent Confident Develop programming skills. Learn to work with a partner or team. Have a positive (this doesn’t mean easy) experience.

BASIC PLAN Select students (usually from courses I’ve recently taught) at end of Fall semester. We work on project during Spring semester. Students present at MathFest in August if sufficient progress was made. Students work on project during Fall semester. Students present at Joint Meetings in January. Students also present at local conferences and at school.

BASIC PLAN Select students (usually from courses I’ve recently taught) at end of Fall semester. We work on project during Spring semester. Students present at MathFest in August if sufficient progress was made. Students work on project during Fall semester. Students present at Joint Meetings in January. Students also present at local conferences and at school. Of course results and progress don’t simply follow such a neat and tidy schedule.

BASICS OF MY PROJECTS Number of students Time Presentations After Pepperdine

BASICS OF MY PROJECTS Number of students Time Presentations After Pepperdine 8 of my 16 research students have gone on to pursue something other than graduate school in mathematics. They still tell me the research experience was of very high value to them.

IS CLOSER ALWAYS BETTER WHEN KICKING FIELD GOALS? Number of students: Two Time: 2004 – 2005 Presentations: 2005 Joint Meetings After Pepperdine: Ph.D. program in mathematics Peace Corps

A COMPARISON OF PRE-SEASON AND FINAL COLLEGE FOOTBALL POLLS Number of students: Three Time: 2007 – 2008 Presentations: 2007 Joint Meetings After Pepperdine: Ph.D. program in mathematics Ph.D. program in financial mathematics Actuary

A SINKHORN-KNOPP FIXED POINT PROBLEM (LINEAR ALGEBRA) Number of students: Four Time: 2008 – 2009 Presentations: 2008 MathFest 2009 Joint Meetings Local conferences After Pepperdine: Ph.D. program in mathematics Masters program in international business Medical school

A COMBINATORICS PROBLEM ARISING IN THE “WICKED” TICKET LOTTERY Number of students: Two Time: 2009 – 2010 Presentations: 2010 Joint Meetings Local conferences After Pepperdine: Masters/Ph.D. program in computer science Masters program in management science and engineering

AN DERIVATIVE APPROXIMATION USING LU FACTORIZATION OF VANDERMONDE MATRICES Number of students: One Time: 2010 – 2011 Presentations: 2010, 2011 MathFest 2011 Joint Meetings Local conferences After Pepperdine: Joint JD/MS program in electrical engineering and CS

IDEAL SEAT LOCATION IN THE ROSE BOWL STADIUM Number of students: One Time: 2011 – 2012 Presentations: 2011 MathFest 2012 Joint Meetings Local conferences After Pepperdine: Actuary

CODING A JAVA APPLET FOR CALCULUS Number of students: One Time: 2013 Presentations: Not applicable After Pepperdine: Not yet graduated

MOSAICKING DIGITAL IMAGES Number of students: Two Time: Presentations: 2014 MathFest, Portland, OR 2015 Joint Meetings, San Antonio, TX After Pepperdine: Ph.D. program in mathematics Student two not yet graduated

FINANCIAL SUPPORT For the majority of these projects I was able to arrange some financial support for students: $10/hour for 10 hours/week for 15 weeks. For most (all?) Joint Meetings and MathFests, Pepperdine supported each student in travel costs (the MAA and PME are quite good about offering support). The students think this is pretty cool. For the group of four students my students had a CURM grant for two semesters. All students receive academic credit of 1 – 4 units, depending on how much time they put in.

SUMMARY OF THE STUDENTS Most of my students went on to graduate school. Of those, about half went in to math, the other half into other disciplines including finance, medical school, business, CS, management science, law/EE. Other pursuits after graduation included actuarial positions and the Peace Corps. These were good students and good people before working with me, and likely would have done good things with or without a research experience. But for all of them the experience was very helpful.

SOME ADVICE Be curious. Keep a list of potential problems that students can help you on. They don’t have to be from your own research area. If appropriate, allow students to help select topic. Projects involving experimentation is nice. It is useful for students to have background in programming. Still, they will pick up some real life experience programming as part of the project.

THREE PROJECTS